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NASA NTRS2017

An Efficient Universal Trajectory Language

The Efficient Universal Trajectory Language (EUTL) is a language for specifying and representing trajectories for Air Traffic Management (ATM) concepts such as Trajectory-Based Operations (TBO). In these concepts, the communication of a trajectory between an aircraft and ground automation is fundamental. Historically, this trajectory exchange has not been done, leading to trajectory definitions that have been centered around particular application domains and, therefore, are not well suited for TBO applications. The EUTL trajectory language has been defined in the Prototype Verification System (PVS) formal specification language, which provides an operational semantics for the EUTL language. The hope is that EUTL will provide a foundation for mathematically verified algorithms that manipulate trajectories. Additionally, the EUTL language provides well-defined methods to unambiguously determine position and velocity information between the reported trajectory points. In this paper, we present the EUTL trajectory language in mathematical detail.

Hagen, George E.↗

NASA NTRS2015

Benefits Assessment for Single-Airport Tactical Runway Configuration Management Tool (TRCM)

The System-Oriented Runway Management (SORM) concept was developed as part of the Airspace Systems Program (ASP) Concepts and Technology Development (CTD) Project, and is composed of two basic capabilities: Runway Configuration Management (RCM), and Combined Arrival/Departure Runway Scheduling (CADRS). RCM is the process of designating active runways, monitoring the active runway configuration for suitability given existing factors, and predicting future configuration changes; CADRS is the process of distributing arrivals and departures across active runways based on local airport and National Airspace System (NAS) goals. The central component in the SORM concept is a tool for taking into account all the various factors and producing a recommendation for what would be the optimal runway configuration, runway use strategy, and aircraft sequence, considering as many of the relevant factors required in making this type of decision, and user preferences, if feasible. Three separate tools were initially envisioned for this research area, corresponding to the time scale in which they would operate: Strategic RCM (SRCM), with a planning horizon on the order of several hours, Tactical RCM (TRCM), with a planning horizon on the order of 90 minutes, and CADRS, with a planning horizon on the order of 15-30 minutes[1]. Algorithm development was initiated in all three of these areas, but the most fully developed to date is the TRCM algorithm. Earlier studies took a high-level approach to benefits, estimating aggregate benefits across most of the major airports in the National Airspace Systems (NAS), for both RCM and CADRS [2]. Other studies estimated the benefit of RCM and CADRS using various methods of re-sequencing arrivals to reduce delays3,4, or better balancing of arrival fixes5,6. Additional studies looked at different methods for performing the optimization involved in selecting the best Runway Configuration Plan (RCP) to use7-10. Most of these previous studies were high-level or generic in nature (not focusing on specific airports), and benefits were aggregated for the entire NAS, with relatively low fidelity simulation of SORM functions and aircraft trajectories. For SORM research, a more detailed benefits assessment of RCM and CADRS for specific airports or metroplexes is needed.

Oseguera-Lohr, Rosa↗

NASA NTRS2013

An Overview of a Trajectory-Based Solution for En Route and Terminal Area Self-Spacing: Fourth Revision

This paper presents an overview of the fourth major revision to an algorithm specifically designed to support NASA's Airborne Precision Spacing concept. This airborne self-spacing concept is trajectory-based, allowing for spacing operations prior to the aircraft being on a common path. Because this algorithm is trajectory-based, it also has the inherent ability to support required-time-of-arrival (RTA) operations. This algorithm was also designed specifically to support a standalone, non-integrated implementation in the spacing aircraft. Revisions to this algorithm were based on a change to the expected operational environment.

Abbott, Terence S.↗

NASA NTRS2000

Stardust Navigation Covariance Analysis

The Stardust spacecraft was launched on February 7, 1999 aboard a Boeing Delta-II rocket. Mission participants include the National Aeronautics and Space Administration (NASA), the Jet Propulsion Laboratory (JPL), Lockheed Martin Astronautics (LMA) and the University of Washington. The primary objective of the mission is to collect in-situ samples of the coma of comet Wild-2 and return those samples to the Earth for analysis. Mission design and operational navigation for Stardust is performed by the Jet Propulsion Laboratory (JPL). This paper will describe the extensive JPL effort in support of the Stardust pre-launch analysis of the orbit determination component of the mission covariance study. A description of the mission and it's trajectory will be provided first, followed by a discussion of the covariance procedure and models. Predicted accuracy's will be examined as they relate to navigation delivery requirements for specific critical events during the mission. Stardust was launched into a heliocentric trajectory in early 1999. It will perform an Earth Gravity Assist (EGA) on January 15, 2001 to acquire an orbit for the eventual rendezvous with comet Wild-2. The spacecraft will fly through the coma (atmosphere) on the dayside of Wild-2 on January 2, 2004. At that time samples will be obtained using an aerogel collector. After the comet encounter Stardust will return to Earth when the Sample Return Capsule (SRC) will separate and land at the Utah Test Site (UTTR) on January 15, 2006. The spacecraft will however be deflected off into a heliocentric orbit. The mission is divided into three phases for the covariance analysis. They are 1) Launch to EGA, 2) EGA to Wild-2 encounter and 3) Wild-2 encounter to Earth reentry. Orbit determination assumptions for each phase are provided. These include estimated and consider parameters and their associated a-priori uncertainties. Major perturbations to the trajectory include 19 deterministic and statistical maneuvers planned for the mission. The spacecraft is three axis stabilized and has unbalanced thrusters for attitude control. Accelerations due to the attitude control system are treated stochastically. The tracking scenario for the study is patterned after the actual schedule employed during the different phases of the mission. Conventional X-band two-way Doppler and SRA range data was simulated and the standard accuracy for these data types was assumed throughout most of the mission. However, a deweighting scheme was used for the Doppler data during times of low Sun-Earth-Probe angles, especially in the case of the DSM. Optical data is assumed to be available starting at 50 days prior to the comet encounter. The optical data will be used to improve the ephemeris of Wild-2, which is considered crucial to properly target the comet flyby. Results of the covariance analysis are presented for all mission phases. Navigation capability will be discussed in terms of the uncertainty in the encounter B-Plane (B.R and B.T) and linearized time of flight. Delivery errors based on the final maneuver prior to the comet encounter will be presented. The most stringent navigation requirement is for the Earth reentry. The uncertainty in the flight path angle must be less than 0.02 degree (orbit determination and maneuver performance) to assure successful recovery of the SRC. Results presented show that this requirement can be met.

Menon, Premkumar R.↗

NASA NTRS2014

Time and Frequency-Domain Cross-Verification of SLS 6DOF Trajectory Simulations

The SLS GNC team and its partners have developed several time- and frequency-based simulations for development and analysis of the proposed SLS launch vehicle. The simulations differ in fidelity and some have unique functionality that allows them to perform specific analyses. Some examples of the purposes of the various models are: trajectory simulation, multi-body separation, Monte Carlo, hardware in the loop, loads, and frequency domain stability analyses. While no two simulations are identical, many of the models are essentially six degree-of-freedom (6DOF) representations of the SLS plant dynamics, hardware implementation, and flight software. Thus at a high level all of those models should be in agreement. Comparison of outputs from several SLS trajectory and stability analysis tools are ongoing as part of the program's current verification effort. The purpose of these comparisons is to highlight modeling and analysis differences, verify simulation data sources, identify inconsistencies and minor errors, and ultimately to verify output data as being a good representation of the vehicle and subsystem dynamics. This paper will show selected verification work in both the time and frequency domain from the current design analysis cycle of the SLS for several of the design and analysis simulations. In the time domain, the tools that will be compared are MAVERIC, CLVTOPS, SAVANT, STARS, ARTEMIS, and POST 2. For the frequency domain analysis, the tools to be compared are FRACTAL, SAVANT, and STARS. The paper will include discussion of these tools including their capabilities, configurations, and the uses to which they are put in the SLS program. Determination of the criteria by which the simulations are compared (matching criteria) requires thoughtful consideration, and there are several pitfalls that may occur that can severely punish a simulation if not considered carefully. The paper will discuss these considerations and will present a framework for responding to these issues when they arise. For example, small event timing differences can lead to large differences in mass properties if the criteria are to measure those properties at the same time, or large differences in altitude if the criteria are to measure those properties when the simulation experiences a staging event. Similarly, a tiny difference in phase can lead to large gain margin differences for frequency-domain comparisons of gain margins.

VanZwieten, Tannen↗

NASA NTRS1979

The computation of isentropic atmospheric trajectories using a 'discrete model' formulation

An explicit technique for calculating atmospheric trajectories is presented as an alternative method to the standard implicit scheme of Danielsen (1961). The technique uses the inviscid equations of motion and the discrete model formulation derived by Greenspan (1972, 1973) to compute trajectories on isentropic surfaces, assuming adiabatic flow. The discrete model formulation is designed specifically for a Lagrangian system and objectively accounts for the geostrophic departures, local psi-tendencies, and the subsequent accelerations along the entire length of the trajectory. Application of the discrete formulation to a diagnostic case study yielded favorable results.

Petersen, R. A.↗

NASA NTRS2016

Global Optimization of Low-Thrust Interplanetary Trajectories Subject to Operational Constraints

Low-thrust electric propulsion provides many advantages for mission to difficult targets-Comets and asteroids-Mercury-Outer planets (with sufficient power supply)Low-thrust electric propulsion is characterized by high power requirements but also very high specific impulse (Isp), leading to very good mass fractions. Low-thrust trajectory design is a very different process from chemical trajectory.

optimization↗

NASA NTRS1961

Effects of Flight Conditions at Booster Separation on Payload Weight in Orbit

A study of the principal flight parameters at booster separation was conducted to find the effect of each on the weight of the payload boosted into an earth orbit along a zero drag gravity turn trajectory. The parameters considered include Mach number (3 to 9), flight-path angle (10 deg to 55 deg), altitude (90,000 and 350,000 ft), inert weight ratio (0.05 to 0.15), and thrust-weight ratio (1.5 to 2.5), with a specific impulse of 289 seconds. Both transfer ellipse and direct orbit trajectories were considered. With either trajectory method, payload weight was highest for low initial flight-path angles and high initial Mach numbers. Of course, high initial Mach numbers require greater energy expenditures from the booster. Changes in initial altitude had little effect on payload weight, and only small gains were evident when thrust-weight ratio was increased.

Nelson, Richard D.↗

NASA NTRS2011

An Overview of a Trajectory-Based Solution for En Route and Terminal Area Self-Spacing to Include Parallel Runway Operations

This paper presents an overview of an algorithm specifically designed to support NASA's Airborne Precision Spacing concept. This airborne self-spacing concept is trajectory-based, allowing for spacing operations prior to the aircraft being on a common path. This implementation provides the ability to manage spacing against two traffic aircraft, with one of these aircraft operating to a parallel dependent runway. Because this algorithm is trajectory-based, it also has the inherent ability to support required-time-of-arrival (RTA) operations

Abbott, Terence S.↗

NASA NTRS2017

Time and Frequency-Domain Cross-Verification of SLS 6DOF Trajectory Simulations

The Space Launch System (SLS) Guidance, Navigation, and Control (GNC) team and its partners have developed several time- and frequency-based simulations for development and analysis of the proposed SLS launch vehicle. The simulations differ in fidelity and some have unique functionality that allows them to perform specific analyses. Some examples of the purposes of the various models are: trajectory simulation, multi-body separation, Monte Carlo, hardware in the loop, loads, and frequency domain stability analyses. While no two simulations are identical, many of the models are essentially six degree-of-freedom (6DOF) representations of the SLS plant dynamics, hardware implementation, and flight software. Thus at a high level all of those models should be in agreement. Comparison of outputs from several SLS trajectory and stability analysis tools are ongoing as part of the program's current verification effort. The purpose of these comparisons is to highlight modeling and analysis differences, verify simulation data sources, identify inconsistencies and minor errors, and ultimately to verify output data as being a good representation of the vehicle and subsystem dynamics. This paper will show selected verification work in both the time and frequency domain from the current design analysis cycle of the SLS for several of the design and analysis simulations. In the time domain, the tools that will be compared are MAVERIC, CLVTOPS, SAVANT, STARS, ARTEMIS, and POST 2. For the frequency domain analysis, the tools to be compared are FRACTAL, SAVANT, and STARS. The paper will include discussion of these tools including their capabilities, configurations, and the uses to which they are put in the SLS program. Determination of the criteria by which the simulations are compared (matching criteria) requires thoughtful consideration, and there are several pitfalls that may occur that can severely punish a simulation if not considered carefully. The paper will discuss these considerations and will present a framework for responding to these issues when they arise. For example, small event timing differences can lead to large differences in mass properties if the criteria are to measure those properties at the same time, or large differences in altitude if the criteria are to measure those properties when the simulation experiences a staging event. Similarly, a tiny difference in phase can lead to large gain margin differences for frequency-domain comparisons of gain margins.

Johnson, Matthew↗

DOE OSTI2025

Ensemble Simulation Techniques and Fast Randomized Algorithms

The major goals of the project were to develop and analyze new ensemble simulation techniques, including trajectory stratification and preconditioned MCMC techniques, as well as develop fast numerical linear algebra techniques closely related to ensemble simulation ideas. The trajectory stratification techniques involve simulating in parallel short trajectory fragments of a Markov process confined to a specific region of space‐time and then patching together the statistics gathered to assemble estimates of very general dynamical properties. We have also developed this approach for rare event simulation and extended the techniques to applications requiring a more general framework (such as electronic structure calculations). The preconditioned MCMC techniques involve simulating multiple Markov chains in parallel and then using information from the ensemble to speed the mixing of each individual chain. The fast randomized linear algebra methods are motivated by the diffusion Monte Carlo technique, but are applicable to finding the dominant eigenvalue of (almost) general matrices. For most non‐negative matrices, the schemes result in an error (compared to the power method) that is constant in the dimension of the problem. For more general matrices, we see a very clear sublinear cost trend in computational tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1972

Parametric analysis of performance and design characteristics for advanced earth-to-orbit shuttles

Performance, trajectory, and design characteristics are presented for (1) a single-stage shuttle with a single advanced rocket engine, (2) a single-stage shuttle with an initial parallel chemical engine and advanced engine burn followed by an advanced engine sustainer burn, (3) a single-stage shuttle with an initial chemical engine burn followed by an advanced engine burn, and (4) a two-stage shuttle with a chemical propulsion booster stage and an advanced propulsion upper stage. The ascent trajectory profile includes a brief initial vertical rise; zero-lift flight through the sensible atmosphere; variational steering into an 83-kilometer by 185-kilometer intermediate orbit; and a fixed, 460-meter per second allowance for subsequent maneuvers. Results are given in terms of burnout mass fractions (including structure and payload), trajectory profiles, propellant loadings, and burn times. These results are generated with a trajectory analysis that includes a parametric variation of the specific impulse from 800 to 3000 seconds and the specific engine weight from 0 to 1.0.

Willis, E. A., Jr.↗

NASA NTRS1985

Energy-modelled climb and climb-dash - The Kaiser technique

F. Kaiser's germinal 1944 report on his 'resultant-height' concept, now known as energy modelling, is reviewed. The data base for the Me. 262 jet fighter is recreated via spline-lattice representation of specific excess power. Minimum-time and 'distance'-climb trajectories are generated in an attempt to check Kaiser's results. Agreement is good for the minimum-time calculations but only qualitative agreement is obtained for the mysterious 'distance climbs' whose documentation is fragmentary. The character of optimal climb-dash trajectories in energy approximation is examined and illustrated.

Merritt, S. R.↗

NASA NTRS1986

Numerical simulation of the flowfield over ice accretion shapes

The primary goals are directed toward the development of a numerical method for computing flow about ice accretion shapes and determining the influence of these shapes on flow degradation. It is expedient to investigate various aspects of icing independently in order to assess their contribution to the overall icing phenomena. The specific aspects to be examined include the water droplet trajectories with collection efficiencies and phase change on the surface, the flowfield about specified shapes including lift, drag, and heat transfer distribution, and surface roughness effects. The configurations computed were models of ice accretion shapes formed on a circular cylinder in the NASA Lewis Icing Research Tunnel. An existing Navier-Stokes program was modified to compute the flowfield over four shapes (2, 5, and 15 minute models of glaze ice, and a 15 minute accumulation of rime ice).

Scott, J. N.↗

NASA NTRS2005

Design and Optimization of Low-thrust Orbit Transfers Using Q-law and Evolutionary Algorithms

Future space missions will depend more on low-thrust propulsion (such as ion engines) thanks to its high specific impulse. Yet, the design of low-thrust trajectories is complex and challenging. Third-body perturbations often dominate the thrust, and a significant change to the orbit requires a long duration of thrust. In order to guide the early design phases, we have developed an efficient and efficacious method to obtain approximate propellant and flight-time requirements (i.e., the Pareto front) for orbit transfers. A search for the Pareto-optimal trajectories is done in two levels: optimal thrust angles and locations are determined by Q-law, while the Q-law is optimized with two evolutionary algorithms: a genetic algorithm and a simulated-annealing-related algorithm. The examples considered are several types of orbit transfers around the Earth and the asteroid Vesta.

low-thrust orbit transfer↗

NASA NTRS2010

Interactions of Ku70/80 with Double-Strand DNA: Energetic, Dynamics, and Functional Implications

Space radiation is a proficient inducer of DNA damage leading to mutation, aberrant cell signaling, and cancer formation. Ku is among the first responding proteins in nucleus to recognize and bind the DNA double strand breaks (DSBs) whenever they are introduced. Once loaded Ku works as a scaffold to recruit other repair factors of non-homologous end joining and facilitates the following repair processes. The crystallographic study of the Ku70/80 heterodimer indicate the core structure of this protein shows virtually no conformational change after binding with DNA. To investigate the dynamical features as well as the energetic characteristics of Ku-DNA binding, we conduct multi-nanosecond molecular dynamics simulations of a modeled Ku70/80 structure and several complexes with two 24-bp DNA duplexes. Free energy calculations show significant energy differences between the complexes with Ku bound at DSBs and those with Ku associated at an internal site of a chromosome. The results also reveal detailed interactions between different nucleotides and the amino acids along the DNA-binding cradle of Ku, indicating subtle binding preference of Ku at specific DNA sequences. The covariance matrix analyses along the trajectories demonstrate the protein is stimulated to undergo correlated motions of different domains once bound to DNA ends. Additionally, principle component analyses identify these low frequency collective motions suitable for binding with and translocation along duplex DNA. It is proposed that the modification of dynamical properties of Ku upon binding with DSBs may provide a signal for the further recruitment of other repair factors such as DNA-PKcs, XLF, and XRCC4.

Hu, Shaowen↗

NASA NTRS2011

Developing a Prototype ALHAT Human System Interface for Landing

The goal of the Autonomous Landing and Hazard Avoidance Technology (ALHAT) project is to safely execute a precision landing anytime/anywhere on the moon. This means the system must operate in any lighting conditions, operate in the presence of any thruster generated regolith clouds, and operate without the help of redeployed navigational aids or prepared landing site at the landing site. In order to reach this ambitious goal, computer aided technologies such as ALHAT will be needed in order to permit these landings to be done safely. Although there will be advanced autonomous capabilities onboard future landers, humans will still be involved (either onboard as astronauts or remotely from mission control) in any mission to the moon or other planetary body. Because many time critical decisions must be made quickly and effectively during the landing sequence, the Descent and Landing displays need to be designed to be as effective as possible at presenting the pertinent information to the operator, and allow the operators decisions to be implemented as quickly as possible. The ALHAT project has established the Human System Interface (HSI) team to lead in the development of these displays and to study the best way to provide operators enhanced situational awareness during landing activities. These displays are prototypes that were developed based on multiple design and feedback sessions with the astronaut office at NASA/ Johnson Space Center. By working with the astronauts in a series of plan/build/evaluate cycles, the HSI team has obtained astronaut feedback from the very beginning of the design process. In addition to developing prototype displays, the HSI team has also worked to provide realistic lunar terrain (and shading) to simulate a "out the window" view that can be adjusted to various lighting conditions (based on a desired date/time) to allow the same terrain to be viewed under varying lighting terrain. This capability will be critical to determining the effect of terrain/lighting on the human pilot, and how they use windows and displays during landing activities. The Apollo missions were limited to about 28 possible launch days a year due to lighting and orbital constraints. In order to take advantage of more landing opportunities and venture to more challenging landing locations, future landers will need to utilize sensors besides human eyes for scanning the surface. The ALHAT HSI system must effectively convey ALHAT produced information to the operator, so that landings can occur during less "optimal" conditions (lighting, surface terrain, slopes, etc) than was possible during Apollo missions. By proving this capability, ALHAT will simultaneously provide more flexible access to the moon, and greater safety margins for future landers. This paper will specifically focus on the development of prototype displays (the Trajectory Profile Display (TPD), Landing Point Designation (LPD), and Crew Camera View (CCV) ), implementation of realistic planetary terrain, human modeling, and future HSI plans.

Hirsh, Robert L.↗

NASA NTRSDate not supplied

GLOW_SunFacing and SBG_Comms Analogous Examples

A Venus orbit insertion sequence to meet various science objectives and end with a stable science orbit. An Earth data downlink opportunities to polar ground stations. Neither are mission specific.

Trajectory↗